Finite Group Databasebeta

← #15624525

Subgroups — #15624525

Order 2816.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#525C211yesmaximal, characteristic
2C22×#66999C211yesmaximal, characteristic, complemented
3#13079449C212yesmaximal, complemented
4#13079443C212yesmaximal, complemented
5#13079438C212yesmaximal, complemented
6#13079420C212yesmaximal, complemented
7#13079400C212yesmaximal, complemented
8#13079394C212yesmaximal, complemented
9#13079389C212yesmaximal, complemented
10#13079371C212yesmaximal, complemented
11#13078562C212yesmaximal, complemented
12#13078541C211yesmaximal, characteristic, complemented
13#13078536C211yesmaximal, characteristic, complemented
14#13078244C212yesmaximal, complemented
15#13078240C212yesmaximal, complemented
16#13077872C212yesmaximal, complemented
17#13077850C211yesmaximal, characteristic, complemented
18D11×#407C211yesmaximal, characteristic, complemented
19C11×#3004C211yesmaximal, characteristic, complemented
20C23×Q8×C11C2211yescharacteristic, complemented
21C2×#41×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C2×C11×#137C2212yescomplemented
24C11×#525C2211yescharacteristic
25#10623359C2211yescharacteristic
26C2×#66999—21no—
27C2×#66999—21no—
28C2×#66999—21no—
29C2×#66999—21no—
30C2×#66999—21no—
31C2×#66999—21no—
32C2×#66999C2212yes—
33C2×#66999C2212yes—
34C2×#66999C2212yes—
35C2×#66999C2212yescomplemented
36C2×#66999C2212yescomplemented
37C2×#66999C2212yescomplemented
38C2×#66995C2212yescomplemented
39#10623322C2211yescharacteristic
40C22×(C2×D11)⋊C4—21no—
41C22×C4⋊Dic11C2211yescharacteristic, complemented
42C22×Dic11⋊C4—21no—
43C2×M16×D11C2212yescomplemented
44#10623187—21no—
45D11×#123—21no—
46#10623158C2211yescharacteristic
47#10623158C2211yescharacteristic
48D11×C22⋊Q8C2211yescharacteristic
49D11×C22⋊Q8C2211yescharacteristic
50#10623137C2211yescharacteristic
51#10623137C2211yescharacteristic
52D11×#121C2211yescharacteristic
53D11×#121C2211yescharacteristic
54D11×#120—21no—
55#10623117—21no—
56#10623078—21no—
57#10623078—21no—
58C4×D4×D11—21no—
59C4×D4×D11—21no—
60#10623055C2211yescharacteristic
61D11×#117C2211yescharacteristic
62C11×#451C2212yescomplemented
63C11×#451C2212yescomplemented
64C11×#448C2212yescomplemented
65C11×#448C2212yescomplemented
66C11×#419C2212yescomplemented
67C11×#407C2211yescharacteristic, complemented
68#10622845C2212yescomplemented
69#10622841C2212yescomplemented
70#10622841C2212yescomplemented
71#10622840C2212yescomplemented
72#10622840C2212yescomplemented
73#10622838C2212yescomplemented
74#10622820C2211yescharacteristic, complemented
75#10622802C2214yescomplemented
76#10622801C2214yescomplemented
77#10622800C2214yescomplemented
78#10622799C2214yescomplemented
79#10622787C2214yescomplemented
80#10622786C2214yescomplemented
81#10622784C2214yescomplemented
82#10622782C2214yescomplemented
83#10622746C2212yescomplemented
84#10622739C2212yes—
85#10622734C2212yescomplemented
86#10622657C2212yescomplemented
87#10622656C2212yescomplemented
88#10622647C2212yescomplemented
89#10622646C2212yescomplemented
90#10622608C2212yescomplemented
91#10622429C2214yescomplemented
92#10622428C2214yescomplemented
93#10622427C2214yescomplemented
94#10622426C2214yescomplemented
95#10622425C2214yescomplemented
96#10622422C2214yescomplemented
97#10622420C2214yescomplemented
98#10622418C2214yescomplemented
99#10622349C2212yescomplemented
100#10622348C2212yescomplemented
101#10622339C2212yes—
102#10622339C2212yescomplemented
103D11×C22⋊C8C2212yes—
104D11×C22⋊C8C2212yescomplemented
105#10622335C2212yescomplemented
106#10622334C2212yescomplemented
107C24×D11D411yescharacteristic
108C2×C11×#41C2311yescharacteristic
109C22×Q8×C11—21no—
110C22×Q8×C11—21no—
111C22×Q8×C11—21no—
112C22×Q8×C11—44no—
113C22×Q8×C11C2312yes—
114C22×Q8×C11C2312yes—
115C22×Q8×C11C2312yes—
116C23×C4×C11—21no—
117C23×C4×C11C2311yescharacteristic
118C23×Dic11—21no—
119C23×Dic11D411yescharacteristic
120#41×D11—44no—
121C2×#4343C2311yescharacteristic
122C2×Q8×D11C2311yescharacteristic
123C2×#4341—21no—
124C2×#4341C2311yescharacteristic
125C2×D4×D11—21no—
126C2×D4×D11—21no—
127C2×D4×D11—21no—
128C2×D4×D11C2311yescharacteristic
129C2×#4339—21no—
130C2×#4339C2311yescharacteristic
131C22×C4×D11—21no—
132C22×C4×D11—44no—
133C22×C4×D11D411yescharacteristic
134C22×C4×D11D411yescharacteristic
135C22×C4×D11D411yescharacteristic
136C22×C4×D11D411yescharacteristic
137C22×C4×D11D411yescharacteristic
138C22×C4×D11D411yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C11×#137—44no—
146C2×C11×Q16C2314yescomplemented
147C2×C11×SD16C2314yescomplemented
148C2×C11×M16C2312yes—
149C11×#123—21no—
150C11×C22⋊Q8C2311yescharacteristic
151C11×C22⋊Q8C2311yescharacteristic
152C11×#121C2311yescharacteristic
153C11×#121C2311yescharacteristic
154C11×#120—21no—
155C4×D4×C11—21no—
156C4×D4×C11—21no—
157C11×#117C2311yescharacteristic
158#67006—21no—
159#66999—22no—
160#66999—22no—
161#66999—22no—
162#66999—22no—
163#66999—22no—
164#66999—22no—
165#66999—22no—
166#66999—22no—
167#66999—22no—
168#66999—22no—
169#66999—22no—
170#66999—22no—
171#66999C2314yes—
172#66999C2314yes—
173#66999C2314yes—
174#66999C2314yes—
175#66999C2311yescharacteristic
176#66999C2311yescharacteristic
177C2×#4326C2314yescomplemented
178#66995—44no—
179C2×#4325C2314yescomplemented
180#66992—21no—
181#66992—21no—
182#66991C2311yescharacteristic
183#66991C2311yescharacteristic
184#66990—21no—
185#66990—21no—
186#66990—21no—
187#66988—21no—
188D4×Dic11—21no—
189D4×Dic11—21no—
190#66983C2311yescharacteristic
191#66983C2311yescharacteristic
192#66982—21no—
193C4×C22⋊D11—21no—
194C4×C22⋊D11—21no—
195C4×C22⋊D11—21no—
196C4×C22⋊D11—21no—
197C2×(C2×D11)⋊C4—22no—
198C2×(C2×D11)⋊C4—22no—
199C2×(C2×D11)⋊C4—22no—
200C2×(C2×D11)⋊C4—22no—
201C2×(C2×D11)⋊C4—22no—
202C2×(C2×D11)⋊C4—22no—
203#66979C2311yescharacteristic
204C2×C4⋊Dic11—21no—
205C2×C4⋊Dic11—21no—
206C2×C4⋊Dic11—21no—
207C2×C4⋊Dic11C2312yes—
208C2×C4⋊Dic11C2312yes—
209C2×C4⋊Dic11C2312yes—
210#66977C2311yescharacteristic
211#66977C2311yescharacteristic
212C2×Dic11⋊C4—22no—
213C2×Dic11⋊C4—22no—
214C2×Dic11⋊C4—22no—
215C2×Dic11⋊C4—22no—
216C2×Dic11⋊C4—22no—
217C2×Dic11⋊C4—22no—
218C2×#4318C2312yes—
219M16×D11—44no—
220C2×#4313C2314yes—
221C2×C8×D11C2314yes—
222#66950C2311yescharacteristic
223#66950C2311yescharacteristic
224#66949—21no—
225#66949—21no—
226#66948C2311yescharacteristic
227#66948C2311yescharacteristic
228#66947—21no—
229#66947—21no—
230#66946—21no—
231#66946—21no—
232#66945C2311yescharacteristic
233#66945C2311yescharacteristic
234C4⋊C4×D11—21no—
235C4⋊C4×D11—21no—
236C4⋊C4×D11C2311yescharacteristic
237C4⋊C4×D11C2311yescharacteristic
238#66939—21no—
239#66937—21no—
240#66937—21no—
241#66936—21no—
242#66936—21no—
243#66935—21no—
244#66935—21no—
245#66935—21no—
246(C22⋊D11)⋊C4—21no—
247(C22⋊D11)⋊C4—21no—
248(C22⋊D11)⋊C4—21no—
249(C22⋊D11)⋊C4—21no—
250C22⋊C4×D11—21no—
251C22⋊C4×D11—21no—
252C22⋊C4×D11—21no—
253C22⋊C4×D11—21no—
254C22⋊C4×D11—21no—
255#66931—21no—
256#66931—21no—
257#66930—21no—
258C4×D44—21no—
259C4×D44—21no—
260#66925—21no—
261C42×D11—21no—
262C11×#103C2314yescomplemented
263C11×#103C2314yescomplemented
264C11×C22⋊C8C2312yes—
265C11×C22⋊C8C2312yes—
266#66899C2314yescomplemented
267#66899C2314yescomplemented
268#66899C2314yescomplemented
269#66896C2314yescomplemented
270C22⋊(C11⋊C8)C2312yes—
271C22⋊(C11⋊C8)C2312yes—
272#66885C2314yescomplemented
273(C2×D11)⋊C8C2314yes—
274(C2×D11)⋊C8C2314yes—
275#66882C2314yescomplemented
276#66881C2314yescomplemented
277#66880C2314yescomplemented
278#66872C2314yescomplemented
279#66871C2314yescomplemented
280#60751—111nomaximal, Sylow
281C24×C11C2×D411yescharacteristic
282C23×D11—24no—
283C23×D11—21no—
284C23×D11—42no—
285C23×D11—42no—
286C23×D11C2×D411yescharacteristic
287C23×D11C2×D411yescharacteristic
288C23×D11C2×D411yescharacteristic
289C23×D11C2×D411yescharacteristic
290C23×D11C2×D411yescharacteristic
291C23×D11C2×D411yescharacteristic
292C11×#41—24no—
293C2×Q8×C11—22no—
294C2×Q8×C11—22no—
295C2×Q8×C11—22no—
296C2×Q8×C11—24no—
297C2×Q8×C11—24no—
298C2×Q8×C11—44no—
299C2×Q8×C11—44no—
300C2×Q8×C11—44no—
301C2×Q8×C11—44no—
302C2×Q8×C11—44no—
303C2×Q8×C11C2411yescharacteristic
304C2×Q8×C11C2414yes—
305C2×D4×C11—21no—
306C2×D4×C11—21no—
307C2×D4×C11—21no—
308C2×D4×C11C2411yescharacteristic
309C22×C4×C11—24no—
310C22×C4×C11—22no—
311C22×C4×C11—22no—
312C22×C4×C11—22no—
313C22×C4×C11—21no—
314C22×C4×C11—44no—
315C22×C4×C11C2×D411yescharacteristic
316C22×C4×C11C2×D411yescharacteristic
317C22×C4×C11C2×D411yescharacteristic
318C22×C4×C11C2411yescharacteristic
319C22×C4×C11C2411yescharacteristic
320C22×C4×C11C2411yescharacteristic
321C2×C22⋊D11—21no—
322C2×C22⋊D11—21no—
323C2×C22⋊D11—21no—
324C2×C22⋊D11—21no—
325C2×C22⋊D11—21no—
326C2×C22⋊D11—21no—
327C2×C22⋊D11—21no—
328C22×Dic11—21no—
329C22×Dic11—22no—
330C22×Dic11—22no—
331C22×Dic11—22no—
332C22×Dic11—42no—
333C22×Dic11—44no—
334C22×Dic11C2×D411yescharacteristic
335C22×Dic11C2×D411yescharacteristic
336C22×Dic11C2×D411yescharacteristic
337C22×Dic11C2×D411yescharacteristic
338C22×Dic11C2×D411yescharacteristic
339C22×Dic11C2×D411yescharacteristic
340#4343—42no—
341Q8×D11—42no—
342#4341—42no—
343#4341—44no—
344D4×D11—42no—
345D4×D11—44no—
346D4×D11—44no—
347D4×D11—44no—
348#4339—24no—
349#4339—44no—
350C2×D44—21no—
351C2×D44—21no—
352C2×D44—21no—
353C2×D44C2411yescharacteristic
354C2×C4×D11—21no—
355C2×C4×D11—21no—
356C2×C4×D11—21no—
357C2×C4×D11—21no—
358C2×C4×D11—21no—
359C2×C4×D11—24no—
360C2×C4×D11—24no—
361C2×C4×D11—42no—
362C2×C4×D11—42no—
363C2×C4×D11—42no—
364C2×C4×D11—42no—
365C2×C4×D11—42no—
366C2×C4×D11—42no—
367C2×C4×D11—42no—
368C2×C4×D11—42no—
369C2×C4×D11—42no—
370C2×C4×D11—42no—
371C2×C4×D11—44no—
372C2×C4×D11C2×D411yescharacteristic
373C2×C4×D11C2×D411yescharacteristic
374C2×C4×D11C2×D411yescharacteristic
375C2×C4×D11C2×D411yescharacteristic
376C2×C4×D11C2×D411yescharacteristic
377C2×C4×D11C2×D411yescharacteristic
378C2×C4×D11C2×D411yescharacteristic
379C2×C4×D11C2×D411yescharacteristic
380C2×C4×D11C2×D411yescharacteristic
381C2×C4×D11C2×D411yescharacteristic
382C2×C4×D11C2×D411yescharacteristic
383C2×C4×D11C2×D411yescharacteristic
384C2×C4×D11C2411yescharacteristic
385C2×C4×D11C2411yescharacteristic
386C2×C4×D11C2411yescharacteristic
387C2×C4×D11C2411yescharacteristic
388C2×Dic22—21no—
389C2×Dic22C2411yescharacteristic
390C11×Q16—44no—
391C11×SD16—44no—
392C11×M16—24no—
393C2×C8×C11C2414yes—
394C11×C4⋊C4—21no—
395C11×C4⋊C4—21no—
396C11×C4⋊C4C2411yescharacteristic
397C11×C4⋊C4C2411yescharacteristic
398C11×C22⋊C4—21no—
399C11×C22⋊C4—21no—
400C11×C22⋊C4—21no—
401C11×C22⋊C4—21no—
402C11×C22⋊C4—21no—
403C42×C11—21no—
404C22⋊Dic11—21no—
405C22⋊Dic11—21no—
406C22⋊Dic11—21no—
407C22⋊Dic11—21no—
408C22⋊Dic11—21no—
409#4326—44no—
410#4325—44no—
411(C2×D11)⋊C4—21no—
412(C2×D11)⋊C4—21no—
413(C2×D11)⋊C4—21no—
414(C2×D11)⋊C4—21no—
415(C2×D11)⋊C4—21no—
416(C2×D11)⋊C4—21no—
417(C2×D11)⋊C4—21no—
418(C2×D11)⋊C4—21no—
419(C2×D11)⋊C4—24no—
420(C2×D11)⋊C4—24no—
421(C2×D11)⋊C4—24no—
422(C2×D11)⋊C4—24no—
423(C2×D11)⋊C4—21no—
424(C2×D11)⋊C4—21no—
425C4⋊Dic11—21no—
426C4⋊Dic11—21no—
427C4⋊Dic11—22no—
428C4⋊Dic11—22no—
429C4⋊Dic11—22no—
430C4⋊Dic11C2414yes—
431C4⋊Dic11C2411yescharacteristic
432C4⋊Dic11C2411yescharacteristic
433Dic11⋊C4—21no—
434Dic11⋊C4—21no—
435Dic11⋊C4—21no—
436Dic11⋊C4—21no—
437Dic11⋊C4—24no—
438Dic11⋊C4—24no—
439Dic11⋊C4—24no—
440Dic11⋊C4—24no—
441Dic11⋊C4—21no—
442Dic11⋊C4—21no—
443C4×Dic11—21no—
444C4×Dic11—21no—
445C4×Dic11—21no—
446#4318—24no—
447C2×C11⋊C8C2414yes—
448#4313—44no—
449C8×D11—44no—
450C2×#525—111no—
451C22×C22⋊Q8—111no—
452#3196—112no—
453#3196—112no—
454#3195—112no—
455#3193—112no—
456#3190—112no—
457#3190—112no—
458#3189—112no—
459#3187—112no—
460#3095—112no—
461#3092—111no—
462#3092—111no—
463#3056—112no—
464#3056—112no—
465#3007—112no—
466#3004—111no—
467#3004D1111yescharacteristic, complemented
468C2×#407—111no—
469C23×C11—22no—
470C23×C11—22no—
471C23×C11—22no—
472C23×C11—21no—
473C23×C11C22×D411yescharacteristic
474C23×C11C22×D411yescharacteristic
475C23×C11C22×D411yescharacteristic
476C22×D11—22no—
477C22×D11—22no—
478C22×D11—22no—
479C22×D11—22no—
480C22×D11—22no—
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11—22no—
485C22×D11—21no—
486C22×D11—41no—
487C22×D11—41no—
488C22×D11—41no—
489C22×D11—41no—
490C22×D11—41no—
491C22×D11—41no—
492C22×D11—41no—
493C22×D11—41no—
494C22×D11—42no—
495C22×D11—42no—
496C22×D11—416no—
497C22×D11—42no—
498C22×D11#13714yescomplemented
499C22×D11C22×D411yescharacteristic
500C22×D11C22×D411yescharacteristic
501C22×D11C22×D411yescharacteristic
502C22×D11C22×D411yescharacteristic
503Q8×C11—24no—
504Q8×C11—24no—
505Q8×C11—22no—
506Q8×C11—44no—
507Q8×C11—44no—
508Q8×C11—44no—
509D4×C11—22no—
510D4×C11—42no—
511D4×C11—42no—
512D4×C11—42no—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—22no—
518C2×C4×C11—21no—
519C2×C4×C11—21no—
520C2×C4×C11—24no—
521C2×C4×C11—21no—
522C2×C4×C11—44no—
523C2×C4×C11—44no—
524C2×C4×C11—44no—
525C2×C4×C11—42no—
526C2×C4×C11C22×D411yescharacteristic
527C2×C4×C11C22×D411yescharacteristic
528C2×C4×C11C22×D411yescharacteristic
529C2×C4×C11H(5,𝔽2)14yes—
530C2×C4×C11C2511yescharacteristic
531C22⋊D11—42no—
532C22⋊D11—42no—
533C22⋊D11—42no—
534C22⋊D11—42no—
535C22⋊D11—42no—
536C22⋊D11—42no—
537C22⋊D11—42no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—21no—
541C2×Dic11—21no—
542C2×Dic11—24no—
543C2×Dic11—21no—
544C2×Dic11—41no—
545C2×Dic11—41no—
546C2×Dic11—41no—
547C2×Dic11—41no—
548C2×Dic11—42no—
549C2×Dic11—44no—
550C2×Dic11—44no—
551C2×Dic11—44no—
552C2×Dic11C22×D411yescharacteristic
553C2×Dic11C22×D411yescharacteristic
554C2×Dic11C22×D411yescharacteristic
555C2×Dic11C22×D411yescharacteristic
556D44—22no—
557D44—42no—
558D44—42no—
559D44—42no—
560C4×D11—22no—
561C4×D11—22no—
562C4×D11—22no—
563C4×D11—22no—
564C4×D11—22no—
565C4×D11—22no—
566C4×D11—22no—
567C4×D11—22no—
568C4×D11—41no—
569C4×D11—41no—
570C4×D11—41no—
571C4×D11—41no—
572C4×D11—41no—
573C4×D11—41no—
574C4×D11—41no—
575C4×D11—41no—
576C4×D11—42no—
577C4×D11—42no—
578C4×D11—42no—
579C4×D11—42no—
580C4×D11—42no—
581Dic22—22no—
582Dic22—42no—
583C8×C11—24no—
584C11⋊C8—24no—
585C22×#41—111no—
586C23×Q8C2×D1111yescharacteristic, complemented
587C24×C4—111no—
588C2×#137—112no—
589C2×#137C2×D1112yescomplemented
590C22×M16—112no—
591#525—111no—
592#525—111no—
593#525—111no—
594#525—111no—
595#525—111no—
596#525—111no—
597#525—111no—
598#525—221no—
599#525—221no—
600#525—221no—
601#525—221no—
602#525C2×D1111yescharacteristic
603C2×#123—221no—
604C2×C22⋊Q8—112no—
605C2×C22⋊Q8—112no—
606C2×C22⋊Q8—112no—
607C2×C22⋊Q8—112no—
608C2×C22⋊Q8—112no—
609C2×C22⋊Q8—112no—
610C2×C22⋊Q8—111no—
611C2×C22⋊Q8—111no—
612C2×C22⋊Q8—221no—
613C2×C22⋊Q8—221no—
614C2×C22⋊Q8—221no—
615C2×C22⋊Q8—221no—
616C2×C22⋊Q8—221no—
617C2×C22⋊Q8—221no—
618C2×#121—111no—
619C2×#121—111no—
620C2×#120—221no—
621C2×C4×D4—221no—
622C2×C4×D4—221no—
623C2×#117—111no—
624C22×C4⋊C4—111no—
625C22×C4⋊C4—221no—
626C22×C22⋊C4—221no—
627#485—114no—
628#485—114no—
629#484—112no—
630#484—114no—
631#484—112no—
632#483—112no—
633#483—114no—
634#483—112no—
635#481—112no—
636#481—112no—
637#480—112no—
638#480—112no—
639#470—114no—
640#470—114no—
641#468—114no—
642#468—114no—
643#467—114no—
644#467—114no—
645#465—114no—
646#465—114no—
647#452—114no—
648#452—114no—
649#451—112no—
650#451—112no—
651#451—114no—
652#451C2×D1112yescomplemented
653#451C2×D1112yescomplemented
654#450—114no—
655#448—112no—
656#448—112no—
657#448C2×D1112yescomplemented
658#448C2×D1112yescomplemented
659#428—112no—
660#428—112no—
661#419—112no—
662#419C2×D1112yescomplemented
663#417—112no—
664#417—112no—
665#407—111no—
666#407—112no—
667#407—112no—
668#407—112no—
669#407C2×D1111yescharacteristic, complemented
670C2×C22⋊C8—112no—
671C2×C22⋊C8—112no—
672C22×C11—28no—
673C22×C11—21no—
674C22×C11—21no—
675C22×C11—21no—
676C22×C11—21no—
677C22×C11—21no—
678C22×C11—21no—
679C22×C11—41no—
680C22×C11—41no—
681C22×C11—41no—
682C22×C11#53412yes—
683C22×C11C2×#13712yes—
684C22×C11#57512yes—
685C22×C11C23×D411yescharacteristic
686C2×D11—21no—
687C2×D11—21no—
688C2×D11—21no—
689C2×D11—21no—
690C2×D11—21no—
691C2×D11—21no—
692C2×D11—21no—
693C2×D11—21no—
694C2×D11—21no—
695C2×D11—21no—
696C2×D11—44no—
697C2×D11—44no—
698C2×D11—44no—
699C2×D11—44no—
700C2×D11—44no—
701C2×D11—44no—
702C2×D11—41no—
703C2×D11—41no—
704C2×D11—41no—
705C2×D11—84no—
706C2×D11C2×#13712yes—
707C2×D11C2×#13712yes—
708C4×C11—21no—
709C4×C11—21no—
710C4×C11—44no—
711C4×C11—41no—
712C4×C11—41no—
713C4×C11—41no—
714C4×C11#53412yes—
715C4×C11C2×H(5,𝔽2)12yes—
716Dic11—21no—
717Dic11—21no—
718Dic11—21no—
719Dic11—21no—
720Dic11—41no—
721Dic11—41no—
722Dic11—41no—
723Dic11—44no—
724C25—111no—
725C2×#41—111no—
726C2×#41—111no—
727C2×#41—111no—
728C2×#41—221no—
729C2×#41—221no—
730C2×#41—444no—
731C2×#41C22×D1111yescharacteristic
732C22×Q8—21no—
733C22×Q8—21no—
734C22×Q8—21no—
735C22×Q8—44no—
736C22×Q8—111no—
737C22×Q8C22×D1112yes—
738C22×Q8C22×D1112yes—
739C22×Q8C22×D1112yes—
740C22×D4—111no—
741C22×D4—221no—
742C22×D4—221no—
743C22×D4—221no—
744C23×C4—21no—
745C23×C4—111no—
746C23×C4—111no—
747C23×C4—111no—
748C23×C4—111no—
749C23×C4—111no—
750C23×C4—111no—
751C23×C4—111no—
752C23×C4—111no—
753C23×C4—111no—
754C23×C4—111no—
755C23×C4—111no—
756C23×C4—111no—
757C23×C4—111no—
758C23×C4—221no—
759C23×C4—221no—
760C23×C4—444no—
761C23×C4C22×D1111yescharacteristic
762#137—44no—
763#137—444no—
764C2×Q16—114no—
765C2×Q16C22×D1114yescomplemented
766C2×SD16—114no—
767C2×SD16C22×D1114yescomplemented
768C2×M16—112no—
769C2×M16—114no—
770C2×M16—444no—
771C2×M16C22×D1112yes—
772C22×C8—114no—
773#123—21no—
774#123—221no—
775#123—221no—
776#123—221no—
777#123—221no—
778#123—221no—
779#123—221no—
780#123—221no—
781C22⋊Q8—114no—
782C22⋊Q8—114no—
783C22⋊Q8—114no—
784C22⋊Q8—114no—
785C22⋊Q8—111no—
786C22⋊Q8—111no—
787C22⋊Q8—111no—
788C22⋊Q8—111no—
789C22⋊Q8—111no—
790C22⋊Q8—111no—
791C22⋊Q8—221no—
792C22⋊Q8—221no—
793C22⋊Q8—221no—
794C22⋊Q8—221no—
795C22⋊Q8—222no—
796C22⋊Q8—222no—
797C22⋊Q8—222no—
798C22⋊Q8—222no—
799C22⋊Q8—222no—
800C22⋊Q8—222no—
801C22⋊Q8—222no—
802C22⋊Q8—222no—
803C22⋊Q8—222no—
804C22⋊Q8—222no—
805C22⋊Q8—222no—
806C22⋊Q8—222no—
807C22⋊Q8C22×D1111yescharacteristic
808C22⋊Q8C22×D1111yescharacteristic
809#121—111no—
810#121—111no—
811#121—111no—
812#121—111no—
813#121—111no—
814#121—111no—
815#121—221no—
816#121—221no—
817#121—221no—
818#121—221no—
819#121C22×D1111yescharacteristic
820#121C22×D1111yescharacteristic
821#120—21no—
822#120—221no—
823#120—221no—
824#120—221no—
825#120—221no—
826#120—221no—
827#120—221no—
828#120—221no—
829C4×D4—21no—
830C4×D4—21no—
831C4×D4—221no—
832C4×D4—221no—
833C4×D4—221no—
834C4×D4—221no—
835C4×D4—221no—
836C4×D4—221no—
837C4×D4—221no—
838C4×D4—221no—
839C4×D4—221no—
840C4×D4—221no—
841C4×D4—221no—
842C4×D4—221no—
843C4×D4—221no—
844C4×D4—221no—
845#117—111no—
846#117—111no—
847#117—111no—
848#117—221no—
849#117—221no—
850#117C22×D1111yescharacteristic
851C2×C4⋊C4—112no—
852C2×C4⋊C4—112no—
853C2×C4⋊C4—112no—
854C2×C4⋊C4—111no—
855C2×C4⋊C4—111no—
856C2×C4⋊C4—221no—
857C2×C4⋊C4—221no—
858C2×C4⋊C4—222no—
859C2×C4⋊C4—222no—
860C2×C4⋊C4—222no—
861C2×C4⋊C4—222no—
862C2×C4⋊C4—222no—
863C2×C4⋊C4—222no—
864C2×C4⋊C4—221no—
865C2×C4⋊C4—221no—
866C2×C4⋊C4—221no—
867C2×C22⋊C4—221no—
868C2×C22⋊C4—221no—
869C2×C22⋊C4—221no—
870C2×C22⋊C4—221no—
871C2×C22⋊C4—221no—
872C2×C22⋊C4—222no—
873C2×C22⋊C4—222no—
874C2×C22⋊C4—222no—
875C2×C22⋊C4—222no—
876C2×C22⋊C4—222no—
877C2×C22⋊C4—222no—
878C2×C42—221no—
879#107—114no—
880#107—114no—
881#106—114no—
882#106—114no—
883#103—114no—
884#103—114no—
885#103—114no—
886#103—114no—
887#103C22×D1114yescomplemented
888#103C22×D1114yescomplemented
889#102—114no—
890#102—114no—
891C22⋊C8—112no—
892C22⋊C8—112no—
893C22⋊C8—114no—
894C22⋊C8—114no—
895C22⋊C8C22×D1112yes—
896C22⋊C8C22×D1112yes—
897C2×C11—22no—
898C2×C11—22no—
899C2×C11—22no—
900C2×C11—81no—
901C2×C11C2×#53411yescharacteristic
902C2×C11C22×#13711yescharacteristic
903C2×C11C2×#57511yescharacteristic
904D11—22no—
905D11—22no—
906D11—41no—
907D11—41no—
908D11—81no—
909C24—111no—
910C24—111no—
911C24—111no—
912C24—111no—
913C24—111no—
914C24—111no—
915C24—224no—
916C24—221no—
917C24—442no—
918C24—442no—
919C24D4×D1111yescharacteristic
920#41—24no—
921#41—224no—
922#41—444no—
923#41—442no—
924#41—444no—
925#41—442no—
926C2×Q8—22no—
927C2×Q8—22no—
928C2×Q8—22no—
929C2×Q8—24no—
930C2×Q8—24no—
931C2×Q8—44no—
932C2×Q8—44no—
933C2×Q8—44no—
934C2×Q8—44no—
935C2×Q8—44no—
936C2×Q8—111no—
937C2×Q8—221no—
938C2×Q8—442no—
939C2×Q8C23×D1111yescharacteristic
940C2×Q8C23×D1114yes—
941C2×D4—21no—
942C2×D4—21no—
943C2×D4—21no—
944C2×D4—111no—
945C2×D4—221no—
946C2×D4—221no—
947C2×D4—221no—
948C2×D4—221no—
949C2×D4—221no—
950C2×D4—221no—
951C2×D4—221no—
952C2×D4—221no—
953C2×D4—221no—
954C2×D4—221no—
955C2×D4—442no—
956C2×D4—444no—
957C2×D4—444no—
958C2×D4—444no—
959C2×D4C23×D1111yescharacteristic
960C22×C4—24no—
961C22×C4—22no—
962C22×C4—22no—
963C22×C4—22no—
964C22×C4—21no—
965C22×C4—44no—
966C22×C4—111no—
967C22×C4—111no—
968C22×C4—111no—
969C22×C4—111no—
970C22×C4—111no—
971C22×C4—111no—
972C22×C4—111no—
973C22×C4—111no—
974C22×C4—111no—
975C22×C4—111no—
976C22×C4—111no—
977C22×C4—111no—
978C22×C4—111no—
979C22×C4—111no—
980C22×C4—111no—
981C22×C4—111no—
982C22×C4—111no—
983C22×C4—111no—
984C22×C4—111no—
985C22×C4—111no—
986C22×C4—111no—
987C22×C4—111no—
988C22×C4—221no—
989C22×C4—221no—
990C22×C4—221no—
991C22×C4—221no—
992C22×C4—221no—
993C22×C4—224no—
994C22×C4—224no—
995C22×C4—222no—
996C22×C4—222no—
997C22×C4—222no—
998C22×C4—221no—
999C22×C4—442no—
1000C22×C4—442no—
1001C22×C4—442no—
1002C22×C4—442no—
1003C22×C4—442no—
1004C22×C4—442no—
1005C22×C4—442no—
1006C22×C4—442no—
1007C22×C4—442no—
1008C22×C4—442no—
1009C22×C4—444no—
1010C22×C4—442no—
1011C22×C4—444no—
1012C22×C4D4×D1111yescharacteristic
1013C22×C4D4×D1111yescharacteristic
1014C22×C4D4×D1111yescharacteristic
1015C22×C4C23×D1111yescharacteristic
1016C22×C4C23×D1111yescharacteristic
1017C22×C4C23×D1111yescharacteristic
1018Q16—44no—
1019Q16—444no—
1020SD16—44no—
1021SD16—444no—
1022M16—24no—
1023M16—224no—
1024M16—444no—
1025C2×C8—114no—
1026C2×C8—444no—
1027C2×C8C23×D1114yes—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—114no—
1031C4⋊C4—111no—
1032C4⋊C4—111no—
1033C4⋊C4—221no—
1034C4⋊C4—221no—
1035C4⋊C4—224no—
1036C4⋊C4—224no—
1037C4⋊C4—224no—
1038C4⋊C4—224no—
1039C4⋊C4—221no—
1040C4⋊C4—221no—
1041C4⋊C4—221no—
1042C4⋊C4—221no—
1043C4⋊C4—222no—
1044C4⋊C4—222no—
1045C4⋊C4—222no—
1046C4⋊C4—221no—
1047C4⋊C4—221no—
1048C4⋊C4C23×D1111yescharacteristic
1049C4⋊C4C23×D1111yescharacteristic
1050C22⋊C4—21no—
1051C22⋊C4—21no—
1052C22⋊C4—21no—
1053C22⋊C4—21no—
1054C22⋊C4—21no—
1055C22⋊C4—221no—
1056C22⋊C4—221no—
1057C22⋊C4—224no—
1058C22⋊C4—224no—
1059C22⋊C4—224no—
1060C22⋊C4—224no—
1061C22⋊C4—221no—
1062C22⋊C4—221no—
1063C22⋊C4—221no—
1064C22⋊C4—221no—
1065C22⋊C4—221no—
1066C22⋊C4—221no—
1067C22⋊C4—221no—
1068C22⋊C4—221no—
1069C22⋊C4—221no—
1070C22⋊C4—221no—
1071C22⋊C4—221no—
1072C22⋊C4—221no—
1073C22⋊C4—221no—
1074C42—21no—
1075C42—221no—
1076C42—221no—
1077C42—221no—
1078C11#6075111yescharacteristic, complemented, Sylow
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—21no—
1083C23—111no—
1084C23—111no—
1085C23—114no—
1086C23—111no—
1087C23—111no—
1088C23—222no—
1089C23—222no—
1090C23—222no—
1091C23—222no—
1092C23—222no—
1093C23—222no—
1094C23—222no—
1095C23—222no—
1096C23—222no—
1097C23—221no—
1098C23—441no—
1099C23—441no—
1100C23—441no—
1101C23—441no—
1102C23—441no—
1103C23—441no—
1104C23—441no—
1105C23—441no—
1106C23—4416no—
1107C23—442no—
1108C23—442no—
1109C23—442no—
1110C23C2×D4×D1111yescharacteristic
1111C23C2×D4×D1111yescharacteristic
1112C23C2×D4×D1111yescharacteristic
1113Q8—24no—
1114Q8—24no—
1115Q8—22no—
1116Q8—44no—
1117Q8—44no—
1118Q8—44no—
1119Q8—222no—
1120Q8—442no—
1121D4—22no—
1122D4—42no—
1123D4—42no—
1124D4—42no—
1125D4—222no—
1126D4—442no—
1127D4—442no—
1128D4—442no—
1129D4—442no—
1130D4—442no—
1131D4—442no—
1132D4—442no—
1133D4—442no—
1134D4—442no—
1135D4—442no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—24no—
1145C2×C4—44no—
1146C2×C4—44no—
1147C2×C4—44no—
1148C2×C4—42no—
1149C2×C4—111no—
1150C2×C4—111no—
1151C2×C4—111no—
1152C2×C4—111no—
1153C2×C4—222no—
1154C2×C4—222no—
1155C2×C4—222no—
1156C2×C4—222no—
1157C2×C4—222no—
1158C2×C4—222no—
1159C2×C4—222no—
1160C2×C4—222no—
1161C2×C4—222no—
1162C2×C4—222no—
1163C2×C4—221no—
1164C2×C4—221no—
1165C2×C4—224no—
1166C2×C4—221no—
1167C2×C4—441no—
1168C2×C4—441no—
1169C2×C4—441no—
1170C2×C4—441no—
1171C2×C4—441no—
1172C2×C4—441no—
1173C2×C4—441no—
1174C2×C4—441no—
1175C2×C4—442no—
1176C2×C4—442no—
1177C2×C4—442no—
1178C2×C4—442no—
1179C2×C4—441no—
1180C2×C4—441no—
1181C2×C4—441no—
1182C2×C4—441no—
1183C2×C4—442no—
1184C2×C4—444no—
1185C2×C4—444no—
1186C2×C4—444no—
1187C2×C4—442no—
1188C2×C4C2×D4×D1111yescharacteristic
1189C2×C4C2×D4×D1111yescharacteristic
1190C2×C4C2×D4×D1111yescharacteristic
1191C2×C4#6703714yes—
1192C2×C4C24×D1111yescharacteristic
1193C8—24no—
1194C8—224no—
1195C22—28no—
1196C22—21no—
1197C22—21no—
1198C22—21no—
1199C22—21no—
1200C22—21no—
1201C22—21no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—112no—
1206C22—112no—
1207C22—221no—
1208C22—221no—
1209C22—221no—
1210C22—221no—
1211C22—221no—
1212C22—221no—
1213C22—221no—
1214C22—221no—
1215C22—221no—
1216C22—221no—
1217C22—444no—
1218C22—444no—
1219C22—444no—
1220C22—444no—
1221C22—444no—
1222C22—444no—
1223C22—441no—
1224C22—441no—
1225C22—441no—
1226C22—884no—
1227C22#1062312012yes—
1228C22D11×#13712yes—
1229C22#1062330812yes—
1230C22C22×D4×D1111yescharacteristic
1231C4—21no—
1232C4—21no—
1233C4—44no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—221no—
1238C4—221no—
1239C4—221no—
1240C4—221no—
1241C4—441no—
1242C4—441no—
1243C4—444no—
1244C4—441no—
1245C4#1062312012yes—
1246C4C2×#6703712yes—
1247C2—22no—
1248C2—22no—
1249C2—22no—
1250C2—81no—
1251C2—222no—
1252C2—222no—
1253C2—441no—
1254C2—441no—
1255C2—881no—
1256C2C2×#1062312011yescharacteristic
1257C2C2×D11×#13711yescharacteristic
1258C2C2×#1062330811yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3004C2
socleC22×C11C23×D4
prime radicalD11×#525C2
hypercenter#3004D11
hypocenterC11#60751
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3004

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×#66999C2semidirect
3. #13079449C2semidirect
4. #13079443C2semidirect
5. #13079438C2semidirect
6. #13079420C2semidirect
7. #13079400C2semidirect
8. #13079394C2semidirect
9. #13079389C2semidirect
10. #13079371C2semidirect
11. #13078562C2semidirect
12. #13078541C2semidirect
13. #13078536C2semidirect
14. #13078244C2semidirect
15. #13078240C2semidirect
16. #13077872C2semidirect
17. #13077850C2semidirect
18. D11×#407C2semidirect
19. C11×#3004C2semidirect
20. C23×Q8×C11C22semidirect
23. C2×C11×#137C22semidirect
35. C2×#66999C22semidirect
36. C2×#66999C22semidirect
37. C2×#66999C22semidirect
38. C2×#66995C22semidirect
41. C22×C4⋊Dic11C22semidirect
43. C2×M16×D11C22semidirect
62. C11×#451C22semidirect
63. C11×#451C22semidirect
64. C11×#448C22semidirect
65. C11×#448C22semidirect
66. C11×#419C22semidirect
67. C11×#407C22semidirect
68. #10622845C22semidirect
69. #10622841C22semidirect
70. #10622841C22semidirect
71. #10622840C22semidirect
72. #10622840C22semidirect
73. #10622838C22semidirect
74. #10622820C22semidirect
75. #10622802C22semidirect
76. #10622801C22semidirect
77. #10622800C22semidirect
78. #10622799C22semidirect
79. #10622787C22semidirect
80. #10622786C22semidirect
81. #10622784C22semidirect
82. #10622782C22semidirect
83. #10622746C22semidirect
85. #10622734C22semidirect
86. #10622657C22semidirect
87. #10622656C22semidirect
88. #10622647C22semidirect
89. #10622646C22semidirect
90. #10622608C22semidirect
91. #10622429C22semidirect
92. #10622428C22semidirect
93. #10622427C22semidirect
94. #10622426C22semidirect
95. #10622425C22semidirect
96. #10622422C22semidirect
97. #10622420C22semidirect
98. #10622418C22semidirect
99. #10622349C22semidirect
100. #10622348C22semidirect
102. #10622339C22semidirect
104. D11×C22⋊C8C22semidirect
105. #10622335C22semidirect
106. #10622334C22semidirect
146. C2×C11×Q16C23semidirect
147. C2×C11×SD16C23semidirect
177. C2×#4326C23semidirect
179. C2×#4325C23semidirect
262. C11×#103C23semidirect
263. C11×#103C23semidirect
266. #66899C23semidirect
267. #66899C23semidirect
268. #66899C23semidirect
269. #66896C23semidirect
272. #66885C23semidirect
275. #66882C23semidirect
276. #66881C23semidirect
277. #66880C23semidirect
278. #66872C23semidirect
279. #66871C23semidirect
467. #3004D11semidirect
498. C22×D11#137semidirect
586. C23×Q8C2×D11semidirect
589. C2×#137C2×D11semidirect
652. #451C2×D11semidirect
653. #451C2×D11semidirect
657. #448C2×D11semidirect
658. #448C2×D11semidirect
662. #419C2×D11semidirect
669. #407C2×D11semidirect
765. C2×Q16C22×D11semidirect
767. C2×SD16C22×D11semidirect
887. #103C22×D11semidirect
888. #103C22×D11semidirect
1078. C11#60751semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D11×#5252
C22×#669992
#130794492
#130794432
#130794382
#130794202
#130794002
#130793942
#130793892
#130793712
#130785622
#130785412
#130785362
#130782442
#130782402
#130778722
#130778502
D11×#4072
C11×#30042
#6075111